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Bayesian inversion for an inverse spectral problem of transmission eigenvalues
The transmission eigenvalue problem plays an important role in the inverse scattering theory of inhomogeneous media. In particular, transmission...
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Inverse nodal problems for singular problems in the half-line
In this paper we study an inverse problem for a singular ordinary differential equation in the half-line. We consider a class of positive weights...
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A Hausdorff-measure boundary element method for acoustic scattering by fractal screens
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what...
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Trace Formula and Inverse Problems
Our aim in this section is to establish an explicit formula allowing one to calculate the Euler characteristic of the metric graph directly from the...
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Inverse Problems for Elliptic Equations
This chapter is an introduction to the basic inverse problems for elliptic equations. One class of these inverse problems arises when the Born...
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Localization of the Discontinuity Lines of the Bottom Scattering Coefficient According to Acoustic Sounding Data
AbstractThe paper considers the mathematical problems of constructing sonar images of the seabed from the data of measurements of a multibeam...
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The Partial Inverse Spectral Problems for a Differential Operator
We firstly study two partial inverse problems for a second-order differential equation with a special boundary condition and recover this operator...
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Inverse Problem of Bitsadze–Samarskii Type for a Two-Dimensional Parabolic Equation of Fractional Order
We consider a nonlocal inverse problem of Bitsadze–Samarskii type for a degenerate fractional order parabolic equation with the Gerasimov–Caputo...
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The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem
We study the global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a...
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Scattering for the Radial Schrödinger Equation with Combined Power-type and Choquard-type Nonlinearities
In this paper, we show the scattering of the radial solution for the nonlinear Schrödinger equation with combined power-type and Choquard-type...
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Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type in a Rectangular Domain
AbstractThe inverse problem of determining the solution and the kernel of the integral term in an inhomogeneous two-dimensional integrodifferential...
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Inverse problems for some fractional equations with general nonlinearity
Inspired by some interesting equations modeling anomalous diffusion and nonlinear phenomena, we will study the inverse problems of uniquely...
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Inverse problems for radial Schrödinger operators with the missing part of eigenvalues
We study inverse spectral problems for radial Schrödinger operators in L 2 (0, 1). It is well known that for a radial Schrödinger operator, two spectra...
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Inverse Spectral and Scattering Theory An Introduction
The aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical...
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Scattering and rigidity for nonlinear elastic waves
For the Cauchy problem of nonlinear elastic wave equations of three-dimensional isotropic, homogeneous and hyperelastic materials satisfying the null...
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On Justification of the Asymptotics of Three One-Dimensional Short-Range Particles Scattering Problem Solution for the Processes 3 → 2
The present paper is a continuation of the three-body one-dimensional scattering problem in the presence of bound states. Full description and...
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Solution of Inverse Problems for Wave Equation with a Nonlinear Coefficient
AbstractTwo hyperbolic equations with a nonlinear coefficient multiplying the highest derivative are considered. The coefficient determines the...
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Scattering problems of impulsive Schrödinger equations with matrix coefficients
In this paper, we set an impulsive boundary value problem for matrix valued Schrödinger equation on the semi axis. We first introduce some solutions...